XOR Triples

Choose distinct integers from 1 to $N$ and collect them into one sequence. For every choice of three distinct chosen numbers $a$, $b$, $c$, the value $a \oplus b \oplus c$ must not be 0, where $\oplus$ is the bitwise exclusive or (XOR).

Find a sequence of maximum length that satisfies this condition.

The first line contains the number of test cases $T$ ($1 \leq T \leq 100$).

Each of the next $T$ lines contains one integer $N$ ($1 \leq N \leq 20$).

Print the answer for each test case on two lines.

• The first line holds the length of the sequence.
• The second line holds the sequence sorted in increasing order, separated by single spaces.

If several sequences reach the maximum length, print only the one that is lexicographically smallest after sorting in increasing order.